Preemptive stochastic online scheduling on uniform machines with bounded speed ratios

We study the preemptive stochastic online scheduling problem on uniformly related machines where jobs are arriving over time. The objective is to minimize total weighted expected completion time. We consider the class of machines sets where the speed ratios have a lower bound. For each set of machines in this class, we design an algorithm with competitive is 2. More specially, we show that the competitive of our algorithm can´t be improved. This generalizes the currently best known result for identical machines and includes the result for two uniform machines obtained by Gu et al.